From a set of 5 column vectors in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjRGJ0Y1RjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=, select a basis, that is, a maximal linearly independent subset.

JSFHSolution by Task TemplateJSFH

In the cell below, use the Matrix palette to generate a sequence of 5 random column vectors in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjRGJ0Y1RjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=.Press the Enter key to generate an equation label.JSFHJSFHTools\342\211\273Tasks\342\211\273Browse:
Linear Algebra\342\211\273Vector Manipulations\342\211\273Basis for a Set of 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LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNictSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JEYrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGMg==

TTdSMApJNlJUQUJMRV9TQVZFLzEzNzMxNTY4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSEiIyIiIiIiI0YoRiY=TTdSMApJNlJUQUJMRV9TQVZFLzEzNzA0MTE4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIyEiIiIiKSIiIkYmTTdSMApJNlJUQUJMRV9TQVZFLzEzNzQ2OTczMlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIiEiJEYoISIlRiY=TTdSMApJNlJUQUJMRV9TQVZFLzEzNzA2MjYyMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIyEiIiIiJCIiIUYmTTdSMApJNlJUQUJMRV9TQVZFLzEzNTkyNDM3MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiJCIiIiEiIiIiI0YmTTdSMApJNlJUQUJMRV9TQVZFLzEzNzA0MTE4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIyEiIiIiKSIiIkYmTTdSMApJNlJUQUJMRV9TQVZFLzEzNzA2MjYyMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIyEiIiIiJCIiIUYmTTdSMApJNlJUQUJMRV9TQVZFLzEzNTkyNDM3MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiJCIiIiEiIiIiI0YmJSFHSolutions from First PrinciplesContext MenuJSFH

Form a matrix whose columns are the five given vectors.Obtain reduced row-echelon form of the matrix.Reference the sequence of vectors by equation label.
Press the Enter key.Context Menu: Conversions \342\211\273 To ListContext Menu:
Select Elements \342\211\273 Combine into MatrixContext Menu:
Solvers and Forms\342\211\273
Row-Echelon Form\342\211\273ReducedJSFHJSFHJSFHJSFHJSFHJSFH